Matching is a classic problem with a rich history and a significant impact on both the theory of algorithms and in practice. Recently, there has been a surge of interest in the online version of matching and its generalizations. This is due to the important new application domain of Internet advertising. The theory of online matching and allocation has played a critical role in designing algorithms for ad allocation. Online Matching and Ad Allocation surveys the key problems, models, and algorithms from online matchings, as well as their implication in the practice of ad allocation. It provides a classification of the problems in this area, an introduction into the techniques used, a glimpse into the practical impact, and ponders some of the open questions that will be of interest in the future. Matching continues to find core applications in diverse domains, and the advent of massive online and streaming data emphasizes the future applicability of the algorithms and techniques surveyed here. Online Matching and Ad Allocation is an ideal primer for anyone interested in matching, and particularly in the online version of the problem, in bipartite graphs.